A child of mass m starts from rest and slides with-out friction from a height h along a curved waterslide(Fig. P5.46). She is launched from a height h/5 into the pool.(a) Is mechanical energy conserved? Why? (b) Give the gravi-tational potential energy associated with the child and herkinetic energy in terms of mgh at the following positions:the top of the waterslide, the launching point, and the pointwhere she lands in the pool. (c) Determine her initial speedh at the launch point in terms of g and h. (d) Determine hermaximum airborne height ymax in terms of h, g, and the hori-zontal speed at that height, w (e) Use the x-component ofthe answer to part (c) to eliminate y from the answer to part(d), giving the height ymax in terms of g, h, and the launchangle 0. (f) Would your answers be the same if the waterslidewere not frictionless? Explain.Утахth/5Figure P5.46

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Answered: A child of mass m starts from rest and…

College Physics

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ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

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Chapter5: Energy

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Problem 46P: A child of mass m starts from rest and slides without friction from a height h along a curved...

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A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (Fig. P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserved? Why? (b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (c) Determine her initial speed V0 at the launch point in terms of g and h. (d) Determine her maximum airborne height ymax in terms of h, g, and the horizontal speed at that height, v0x. (e) Use the x-component of the answer to part (c) to eliminate from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle . (f) Would your answers be the same if the waterslide were not frictionless? Explain. Figure P5.46
A block of mass m = 5.00 kg is released from rest from point and slides on the frictionless track shown in Figure P5.36. Determine (a) the blocks speed at points and and (b) the net work done by the gravitational force on the block as it moves from point from to . Figure P5.36
The system shown in Figure P5.43 is used to lift an object of mass m = 76.0 kg. A constant downward force of magnitude F is applied to the loose end of the rope such that the hanging object moves upward at constant speed. Neglecting the masses of the rope and pulleys, find (a) the required value of F, (b) the tensions T1, T2, and T3, and (c) the work done by the applied force in raising the object a distance of 1.80 m. Figure P5.43
As a young man, Tarzan climbed up a vine to reach his tree house. As he got older, he decided to build and use a staircase instead. Since the work of the gravitational force mg is path Independent, what did the King of the Apes gain in using stairs?
If the net work done by external forces on a particle is zero, which of the following statements about the particle must be true? (a) Its velocity is zero. (b) Its velocity is decreased. (c) Its velocity is unchanged. (d) Its speed is unchanged. (e) More information is needed.
A block of mass m = 2.50 kg is pushed a distance d = 2.20 m along a frictionless, horizontal table by a constant applied force of magnitude F = 16.0 N directed at ail angle = 25 below the horizontal as shown in Figure P7.5. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, (c) the gravitational force, and (d) the net force on the block.
A block of mass m = 2.50 kg is pushed a distance d = 2.20 m along a frictionless, horizontal table by a constant applied force of magnitude F = 16.0 N directed at an angle = 25.0 below the horizontal as shown in Figure P6.3. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, (c) the gravitational force, and (d) the net force on the block. Figure P6.3
How much energy is lost to a dissipative drag force if a 60-kg person falls at a constant speed for 15 meters?
At the start of a basketball game, a referee tosses a basketball straight into the air by giving it some initial speed. After being given that speed, the ball reaches a maximum height of 4.25 m above where it started. Using conservation of energy, find a. the balls initial speed and b. the height of the ball when it has a speed of 2.5 m/s.
Repeat the preceding problem, but this time, suppose that the work done by air resistance cannot be ignored. Let the work done by the air resistance when the skier goes from A to B along the given hilly path be —2000 J. The work done by air resistance is negative since the air resistance acts in the opposite direction to the displacement. Supposing the mass of the skier is 50 kg, what is the speed of the skier at point B ?
A certain automobile engine delivers 2.24 104 W (30.0 hp) to its wheels when moving at a constant speed of 27.0 m/s ( 60 mi/h). What is the resistive force acting on the automobile at that speed?
A 5.0-kg block is pushed 3.0 m up a vertical wall with constant speed by a constant force of magnitude F applied at an angle of = 30 with the horizontal, as shown in Figure P5.76. If the coefficient of kinetic friction between block and wall is 0.30, determine the work done by (a) , (b) the force of gravity, and (c) the normal force between block and wall, (d) By how much does the gravitational potential energy increase during the blocks motion? Figure P5.76

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